Problem: The equation of a circle $C$ is $x^2+y^2+10x+18y+97 = 0$. What is its center $(h, k)$ and its radius $r$ ?
Explanation: To find the equation in standard form, complete the square. $(x^2+10x) + (y^2+18y) = -97$ $(x^2+10x+25) + (y^2+18y+81) = -97 + 25 + 81$ $(x+5)^{2} + (y+9)^{2} = 9 = 3^2$ Thus, $(h, k) = (-5, -9)$ and $r = 3$.